(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(+(x, 0)) → f(x)
+(x, +(y, z)) → +(+(x, y), z)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive path order with status [RPO].
Precedence:
f1 > +2
0 > +2
Status:
f1: multiset
0: multiset
+2: [2,1]
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(+(x, 0)) → f(x)
+(x, +(y, z)) → +(+(x, y), z)
(2) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(3) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(4) TRUE